The art of controlling chaotic processes is in a rudimentary state of development. A chaotic process is defined as one which is deterministic in nature, but nevertheless difficult or impossible to predict because its behavior over time is described by an a periodic function. An example of such a process which is regularly encountered in actual industrial practice is the manufacture of steel from scrap metal by means of an arc furnace. Such furnaces employ very large electrical currents, delivered by heavy graphite electrodes, to melt a violent cauldron of material under controlled temperature conditions over an extended process cycle. Despite the violent conditions inherent in such a process, precise control over the electrical parameters thereof is essential, not only to improve the quality of the steel end product, but also to keep the large process costs in check. And, because of these violent conditions, precise control is an essential safety requirement.
The amount of electrical power typically employed in a large steel-making arc furnace is so great that it is comparable to the usage of an entire city. The currents involved are comparable to a lightning stroke, and far greater in duration. Nevertheless, the temperature and current profiles of each "heat" of steel must be fairly controlled over the duration of the melt in order to determine the nature of the steel produced. In addition, the current drawn by each of the electrodes must be limited for reasons of economy, because the electric "bill" attendant upon such processes is a major cost for the steel producer. The accepted method for controlling the electrode current in large arc furnaces is by dynamically adjusting the arc length through the continuous raising and lowering of the graphite electrodes, of which there are typically three for each furnace.
The penalties for failure to control the positions of the electrodes with sufficient accuracy are severe. If the electrode is not lowered enough, and the arc length consequently is allowed to become too great, the arc may sputter and even be extinguished, thus seriously interfering with the processing of the "heat." If the electrode is lowered too much, so that the arc length becomes too short, not only is excessive current consumed, which is expensive, but the graphite material of the electrode is consumed too rapidly, which also unnecessarily adds to the cost of steel production. Power consumption can be as high as 550 KWH per ton of steel produced, and the cost of electrode consumption is typically of the order of 6 cents per pound of steel produced. Excessive arc currents are also associated with greater rates of electrical component failure. In the extreme case the arc length may be reduced to zero, causing the electrode to become short-circuited to the contents of the furnace, and interrupting the processing thereof. If the arc flashes over to the refractory walls of the furnace, moreover, the latter may be consumed too rapidly or even damaged, resulting in additional repair costs and down time.
Through experience, the art has developed a set of rules of thumb which tell us when to raise and lower the electrodes in order to avoid these catastrophes. These rules are dependent upon the measurement of certain electrical parameters of the arc power supply which have been found empirically to have predictive value, for reasons which are imperfectly understood. See, for example, Persson U.S. Pat. No. 4,620,308; Persson, "Analyzing the Electrical Characteristics of Arc Furnaces," 47th Electric Furnace Conference (1989); Bliss & Harper, "Optimization of Electric Arc Furnace electrode Control Through Closed Loop Control," AISE Iron and Steel Exposition (1989).
These rules of thumb are stored in a conventional rule-based "expert systems" device which keeps track of the time profile of the heat and also monitors running measurements of the predictive electrical parameters, and based on that information outputs a set of desired set-points for those parameters. A device of this type is presently available on the market from the Milltech-HOH Company of Davenport, Iowa under the trademark CONTROLTECH II. This device consists of, among other things, a microcomputer and its associated I/O devices, a power transducer subsystem capable of acquiring all necessary volt, ampere, watt, watt-hour, and power factor signals from an operating arc furnace, and an output subsystem which is capable of continuously adjusting the furnace regulator set-points for each phase of the electrode power supply.
The set-point output of the CONTROLTECH II device is directed to a furnace regulator device, which responds to this information by developing drive output signals which cause the furnace electrode control mechanisms to raise and/or lower each of the furnace electrodes according to a selected control algorithm which is designed to maintain the parameters as close as possible to the set-points presently directed by the rule-based device. A prior-art furnace controller of this type which is in common use at the present time is available from the Robicon Corporation of Pittsburgh, Pa. See U.S. Pat. No. 4,029,888.
Such prior-art furnace regulators do not have the ability to "learn" or otherwise improve their performance over time as a result of operating experience. They are forever limited to the inherent capabilities of a fixed control algorithm which is built in to the regulator circuitry, and thus never changes, short of a redesign and replacement of the regulator circuit hardware. If such a furnace regulator were realized in software, it would of course have a greater measure of flexibility, in that an improvement in the control algorithm could be implemented without a change in hardware, but rewriting and debugging of the source code, recompilation to generate new object code, and reinstallation and retesting of the new algorithm would still be necessary.
An "artificial intelligence" technology is available, however, which has the ability to "learn" from experience or "train" itself to improve its own performance automatically, i.e. without any kind of operator intervention or modification either of a hardware or a software nature. Often referred to as "artificial neural network" technology, this approach can be implemented either in hard-wired circuitry or simulated in software on conventional general-purpose programmable binary digital computers, including even the personal computers which are in common use today, such as Apple Macintosh or IBM-PC computers and compatibles (although in such cases greater than normal amounts of memory or co-processing speed and capacity may be necessary or advisable).
This neural network technology involves the use of multi-valued logic circuits, each of which simulates a biological neuron in the sense that it is activated in response to multi-valued or weighted inputs. Thus, neural circuits are not limited to the two discrete input values characteristic of the binary logic circuitry found in the vast majority of conventional digital computers which are in common use today. A plurality of these logic circuits are typically connected to each other to form a layer, and a number of such layers are normally connected together to form a network including an input (or bottom) layer, an output (or top) layer, and at least one hidden layer interposed between the input and output layers. Lapedes & Farber, "How Neural Nets Work," Neural Information Processing Systems pp. 442-456 (1988). The internal algorithm of the network can be changed by altering the weights assigned to various connections between the outputs of a lower layer and the inputs of a layer above it.
This type of circuitry is especially powerful when the alteration of the weights is done automatically as a function of a control error measurement, because then the control algorithm of the network converges over time to a form that not even the programmer of the original network configuration could have predicted in advance. See Widrow & Hoff, "Adaptive Switching circuits, " 1960 IRE Wescon Convention Record, part 4, pp. 96-104 (1960). Among the weight-modification algorithms which have been recognized in the literature are the gradient descent search technique known as the back-propagation method. See Rumelhart, Hinton & Williams, "Learning Internal Representations by Error Propagation," in Rumelhart & McClelland, "Parallel Distributive Processing: Explorations in the Microstructure of Cognition," vol. 1, MIT Press (1986); Rumelhart, Hinton & Williams, "Learning Representations by Back-Propagating Errors," Nature 323:533-536 (1986). A particular variant of that algorithm has been described in Minai & Williams, "Back-Propagation Heuristics: A Study of the Extended Delta-Bar-Delta Algorithm," IJCNN, vol 1, pp. 595-600 (1990).
It is understood in the art that neural networks and the back-propagation method of "on-the-job training" can be implemented in software on conventional programmable digital computers. In addition, there is at least one commercially available development program which runs under the popular MS-DOS operating system on ordinary IBM-compatible personal computers, and is designed for the development of neural network simulations which employ the back-propagation method and the Delta-Bar-Delta algorithm for self-modification of the network'sinternal control function.